PlanetMath: diagonally dominant matrix

(more info)

Math for the people, by the people.

Main Menu

diagonally dominant matrix

(Definition)

Let be a square matrix of order with entries $a_{ij}$ which are real or complex. Then is said to be diagonally dominant if

$\displaystyle \vert a_{ii}\vert \geq \sum^n_{j=1, j\neq i} \vert a_{ij}\vert$

for

from

is said to be strictly diagonally dominant if

$\displaystyle \vert a_{ii}\vert > \sum^n_{j=1, j\neq i}\vert a_{ij}\vert$

for

from

"diagonally dominant matrix" is owned by Daume.

(view preamble)

Other names:

diagonally dominant, strictly diagonally dominant

Also defines:

strictly diagonally dominant matrix

Attachments:: properties of diagonally dominant matrix (Result) by Andrea Ambrosio

Log in to rate this entry.
(view current ratings)

Cross-references: addition, complex, real, order, square matrix
There are 3 references to this entry.

This is version 4 of diagonally dominant matrix, born on 2003-07-26, modified 2006-07-20.
Object id is 4512, canonical name is DiagonallyDominantMatrix.
Accessed 15628 times total.

Classification:

15-00 (Linear and multilinear algebra; matrix theory :: General reference works )

Pending Errata and Addenda

None.[ View all 3 ]

Discussion

forum policy

No messages.

Interact